27 But, to explain the point in hand: If Christ, in adding the words, "But I say unto you," to the quotations He makes of ancient sayings, neither fulfilled the law of primitive times by His additions, nor destroyed the law given to Moses by opposite precepts, but rather paid such deference to the Hebrew law in all the quotations He made from it, as to make His own remarks chiefly explanatory of what the law stated less distinctly, or a means of securing the design intended by the law, it follows that from the words, "I came not to destroy the law, but to fulfill it" we are not to understand that Christ by His precepts filled up what was wanting in the law; but that what the literal command failed in doing from the pride and disobedience of men, is accomplished by grace in those who are brought to repentance and humility.
The fulfillment is not in additional words, but in acts of obedience. So the apostle says "Faith works by love;" and again, He that loves another has fulfilled the law." This love, by which also the righteousness of the law can be fulfilled was bestowed in its significance by Christ in His coming, through the spirit which He sent according to His promise; and therefore He said, "I came not to destroy the law, but to fulfill it." This is the New Testament in which the promise of the kingdom of heaven is made to this love; which was typified in the Old Testament, suitably to the times of that dispensation. So Christ says again; "A new commandment I give unto you, that you love one another."
Source: Reply to Faustus the Manichaean (New Advent)